Staffer Day Template

1
Information Theory for Mobile Ad-Hoc Networks
(ITMANET) The FLoWS Project
Thrust 1
2
Unequal Error Protection Application and
Performance Limits
S. Borade, B. Nakiboglu, L. Zheng

• bits as the universal measure of information
  and interface to physical layer a homogenous
  view.
• High priority control messages are sent over
  separated channels.
• No performance limits on UEP
• Perfect reliability assumed on network controls

• Complete UEP tradeoff with geometric approach
• Data driven network controls, Layering and QoS
  as interface

• MAIN RESULT
• Optimizing the overall resource, the reliability
  of control signals has a threshold effect
• Communicating at capacity, not even a single bit
  can be protected with positive exponent
• Message-wise prioritization yields better
  tradeoffs than bit-pipe partitioning.
• HOW IT WORKS
• Protecting special message is much easier than
  special bit
• With feedbacks, a two-phase scheme can be used,
  where critical message is used to initiate
  retransmissions

New interface to the physical layer leads to more
flexible higher layer functionalities, and system
level optimizations the new interface also needs
to be backward compatible to bit based networks

• Joint coding allows flexible resource
  allocation
• Priority of critical data in the form/costs of
  better error protections
• Global optimization of resource allocation among
  heterogeneous data

Better tradeoff in UEP has significant effects on
overall system performance
Embedding control messages/significant data with
UEP
3
Towards Strong Converses for MANETs Moulin

• MAIN ACHIEVEMENT
• Derived capacity region for multiple-access
  Gelfand-Pinsker channel. The GP channel models
  transmission in the presence of known
  interference
• HOW IT WORKS
• A set of typical channel outputs is defined.
• A sphere packing analysis is conducted to bound
  the number of codewords that can be packed based
  on the requirement that the error probability is
  small for exponentially many codewords.
• The approach is based on elementary statistics of
  the difference between empirical mutual
  informations (aka self-informations of
  codewords, or information densities)
• ASSUMPTIONS AND LIMITATIONS
• Memoryless channel, but this is not a
  fundamental limitation of the approach

This has been verified for a few problems
(Verdus information spectrum, and Moulins
fingerprinting problem)

New tools are needed to derive tighter outer
bounds on capacity regions
4
Information Theory for Mobile Ad-Hoc Networks
(ITMANET) The FLoWS Project
Thrust 2
5
Indecomposable Finite-State Channels With
Feedback Ron Dabora and Andrea Goldsmith
Understand how to combine code synchronization
into the design of communication networks with
Markov dynamics Identify classes of
inhomogeneous indecomposable FSCs for which
feedback achieves the maximum over all initial
states

• MAIN ACHIEVEMENT
• We identified classes of practical channels
  that can be modeled as indecomposable FSCs. We
  showed that their capacity with feedback is equal
  to the maximum over all channel states.
• HOW IT WORKS
• We identified classes of practical channels
  that can be modeled as indecomposable FSCs. We
  showed that their capacity with feedback is equal
  to the maximum over all channel states.
• ASSUMPTIONS AND LIMITATIONS
• The previous state contains all the past
  information. The current output and state depends
  on both the current input and previous state.

• Many practical communication channels are
  represented as inhomogeneous indecomposable FSCs
• When feedback is present, the capacity of
  indecomposable channels does not achieve the
  maximum over all states.

Introduce the notion of weakly indecomposable
FSCs, i.e., FSC that are indecomposable only
without feedback Capacity of indecomposable FSCs
with feedback can be found without searching over
all channels states Coding schemes that
incorporate Tx-Rx synchronization into the code
can achieve the maximum over all states for
certain indecomposable channels

• Extension to multiuser channels with feedback
• Translation of the results obtained for the
  discrete channel to Gaussian channels with ISI
  and feedback

Most communication channels are subject to
correlated time variations
6
Mutual information and estimation in channelsof
exponential family type Coleman and Raginsky
New results on broadcast and secrecy
capacity without relying on explicit degradation
assumptions. New results on mutual information
and estimation beyond the AWGN channel and
squared error criterion.

• MAIN ACHIEVEMENT
• Analysis of dependence of mutual information
  on channel quality reduces to an
  estimation-theoretic problem with distortion
  function r(x,y)
• HOW IT WORKS
• Structure of E-type channels leads to a dual
  estimation-theoretic characterization of mutual
  information as the minimum rate needed to
  describe the channel output with a given
  constraint on Er(X,Y)
• We can leverage this duality to prove
  monotonicity of I(XY) w.r.t. b under an
  additional (reasonable) assumption on the
  behavior of posterior estimators
• ASSUMPTIONS AND LIMITATIONS
• For a general E-type channel, can prove
  montonicity of mutual info only in high-SNR
  (high-b) regime

How does channel quality impact performance?
Need to explicitly assume channel family is
ordered by degradation Need to check
appropriate conditions on case-by-case basis

• Many channels have this exponential family
  structure. Can connect information theory to
  estimation theory and statistics.
• Exploit maximum entropy character of exponential
  families
• Instead of degradation, exploit the
  b-monotonicity of information gain

Explore connections between information theory
and statistics of E-type channels to obtain new
performance results in the network setting.
New insights into information/estimation lead to
robust design principles for MANETs.
7
Dynamics and Control Principles for Feedback
Encoder DesignsColeman

• Provides explict capacity-achieving recursvie
  encoders for degraded broadcast channels
• Can be extended to many networks with tight
  converses

MAIN RESULT
101
Stochastic Control and Lyapunov theory combined
with converse theorems provide a canonical
methodology to design low-complexity iterative
encoders with feedback in MANETs that achieve
capacity
The use of feedback is of the utmost importance
in designing scalable, robust, reliable
communication schemes Design principles for
provably good iterative feedback encoders
(essentially) limited to Gaussian scenarios
111

• Converse to coding theorems with feedback
  directly guides us how encoders should operate
• State of the system is posterior distribution
  on message given
• Feedback encoder should be interpreted as a
  controller, trying to drive state to certainty.
• Formulate a stochastic control problem and find
  optimal policy

101

• HOW IT WORKS
• Converse theorems specify a stochastic control
  problem. An optimal policy implies the existence
  of a Lyapunov function
• The KL divergence acts as a Lyapunov function on
  the state of the system
• This directly implies achievabililty of all rates
  in capacity region with this explicit iterative
  encoding scheme

111

• Use Stochastic Control methodology for a
  principled, canonical approach to address
• noisy feedback (POMDP)
• Unknown channel (Q-learning)
• Delayed feedback

Xn
Y1 . Yn

• ASSUMPTIONS AND LIMITATIONS
• Noiseless feedback
• Memoryless Channels

A Canonical Controls Methodology to Design
Iterative Feedback Coding Systems in MANETs
8
Optimal ARQ Protocol For Multihop MIMO Relay
Networks Yao Xie, Deniz Gunduz, Andrea Goldsmith
Found optimal ARQ protocol in multihop
MIMO relay networks. Characterized DMDT surfaces
provide insights for practical optimal ARQ
protocols design.

• MAIN RESULTS
• 3D DMDT Surfaces for Various ARQ protocols
  ((4,1,3) system)
• ASSUMPTIONS AND LIMITATIONS
• Long-term/short-term static channel

diversity
What is the rate-reliability-delay tradeoff in
multihop MIMO relay network?
Fractional variable
L 1
rate
Block variable

• There are
• Diversity-multiplexing tradeoff (DMT) analysis
  for relay channel
• Diversity-multiplexing-delay tradeoff (DMDT) for
  point-to-point MIMO with ARQ

Block Variable ARQ
Fractional Variable ARQ
L 10
(2,2,2) system
Long-term

• We characterize the diversity-multiplexing-delay
  tradeoff (DMDT) surface for various ARQ protocols
  
• Theorem the fractional variable ARQ protocol
  achieves optimal DMDT
• Relay should talk ASAP

ARQ 1
ARQ 2
diversity
How it works ARQ protocols in ARQ MIMO relay
networks
H2
H1
Short-term
Optimal Operational Point
rate

• Optimal ARQ protocol for general relay network
• Effects of power control
• Joint source-channel coding in MIMO relay network

ARQ provides one more dimension of tradeoff in
MIMO relay networks.
9
The Multi-Way Relay ChannelDeniz Gündüz, Aylin
Yener, Andrea Goldsmith and Vincent Poor
Exact capacity regions are hard to obtain even
with three nodes. Random codes are capacity
achieving for many models. Decode-and-forward
relaying used in most practical systems.

• Consider inter and/or intra cluster reception
• Combine structured and random codes
• Characterize non-symmetric achievable rate points

MAIN RESULT MODEL Clusters of users
Each user in a cluster wants messages of all
other users in the same cluster. Communication
is enabled by the relay. ASSUMPTIONS AND
LIMITATIONS No signal received from other
users Symmetric capacity for a symmetric
system is analyzed Achievable symmetric rate
is characterized and compared to the upper bound
Joint source-channel coding techniques to achieve
higher rates Structured codes might provide
higher rates than random coding in some networks

• Can we scale structured codes to multiple users?
• Design of practical codes based on joint
  source-channel coding techniques

Compress-and-forward relaying achieves symmetric
rates within a constant gap of capacity. This
gap decays with increasing number of users.
10
Random Linear Network Coding for Time Division
Duplexing (TDD) Lucani, Médard,
Stojanovic

• Novel network coding strategy for TDD
• Use of feedback (ACK) improves delay/energy/
  throughput performance, especially for high
  latency- high errors scenarios
• Random linear coding allows extension to networks

MAIN RESULTS Novel network coding scheme for TDD
channels 1. Delay and Energy Analysis for Link
and Broadcast cases 2. Exists optimal
transmission time in terms of minimizing block
delay, with close-to-optimal energy performance.
3. Outperforms Selective Repeat schemes in high
latency- high error scenarios. Similar
performance otherwise. 4. Delay/throughput
is close to full duplex network coding,
requiring much less energy

• Network coding has studied throughput or delay
  performance considering minimal feedback
• TDD has used ARQ/FEC schemes

1. Use feedback to improve delay performance ACK
states required number of coded packets to decode
data
2. Transmit coded packets for some time, stop to
wait for ACK
HOW IT WORKS 1. Transmission time computed to
minimize delay in data block transmissions, using
ACK and channel conditions 2. Stop transmission
to wait for ACK from receiver (s).
ACK used to update transmission time

• Extend broadcast effect of clusters of
  cooperative nodes
• Sensitivity analysis
• Extend to general network scenario

3. Transmission time depends on ACK and channel
conditions Exists optimal choice
ASSUMPTIONS AND LIMITATIONS Random linear
coding, prior knowledge/estimate of propagation
delay and errors
Feedback, coding and optimal choice of
transmission time minimizes delay, while keeping
throughput performance similar or better than
typical TDD ARQ schemes
11
Layered Source-Channel Schemes A
Distortion-Diversity Perspective Medard, Zheng

• Three-layer scheme dominates previous
  double-layer schemes
• Distortion-diversity tradeoff provides useful
  comparison in different operating regions

• MAIN ACHIEVEMENT
• A three-layer source-channel scheme, which
  includes previous multi-resolution-based and
  multi-description-based schemes as special cases
• HOW IT WORKS
• Multi-description source code with a common
  refinement component
• Superposition coding with successive interference
  cancellation
• Joint source-channel decoding exploits source
  code correlation
• ASSUMPTIONS AND LIMITATIONS
• Quasi-static block-fading channel
• Receivers have perfect channel state information,
  but the transmitter only has statistical
  knowledge of the channel

• Conventional source-channel scheme achieves a
  single level of reconstruction
• Diversity is usually achieved in the channel
  coding component

• Diversity can be achieved through source coding
  techniques, like multiple description codes
• We characterize source-channel schemes with
  distortion-diversity tradeoff

• Extend multi-description-based source-channel
  scheme while preserving the interface between
  source and channel coding
• More general channel model

Distortion-diversity tradeoff better
characterizes layered source-channel schemes
12
The Capacity Region of the Cognitive
Z-interference Channel with a Noiseless
Non-cognitive LinkNan Liu, Ivana Maric, Andrea
Goldsmith and Shlomo Shamai
ACHIEVEMENT DESCRIPTION
Capacity of networks with cognitive users are
unknown. Consequently, optimal ways how to
operate such networks are not understood, nor it
is clear how cognitive nodes should exploit the
obtained information. IT channel models
suitable for networks with cognitive users still
need to be proposed. Capacity of Z-interference
channel is still unknown. Z-interference
channel

• MAIN ACHIEVEMENT
• 1) The capacity region of the discrete cognitive
  Z- interference channel with a noiseless
  non-cognitive link2) An inner and outer bound
  for the cognitive Z-interference channel
• 3) Solution to the generalized Gelfand-
  Pinsker (GP) problem in which a
  transmitter-receiver pair communicates in the
  presence of interference non causally known to
  the encoder. Our solution determines the optimum
  structure of interference.
• HOW IT WORKS
• Non-cognitive encoder uses superposition coding
  to enable partial decoding of interference. The
  cognitive encoder precodes against the rest of
  interference using GP encoding.
• ASSUMPTIONS AND LIMITATIONS
• The considered channel model

1) Optimal scheme for some channels 2)
Superposition coding and Gelfand-Pinsker
coding may be required in order to
minimize interference, in some channels. This
is in contrast to the Gaussian
channel. 3) For the GP problem, the optimal
interference has a superposition structure
STATUS QUO
IMPACT
W1
W1
dest1
source 1
W2
W2
dest2
source 2

• Evaluate a numerical example
• Apply proposed encoding scheme to larger
  networks and to different cognitive node models

NEXT-PHASE GOALS
In some scenarios, interference can be minimized
by exploiting the structure of interference and
cognition at the nodes. Cognition should be used
by the encoder to precode against part of the
interference caused to its receiver.
W1, W2
W1
dest1
cognitive encoder
NEW INSIGHTS
W2
W2
non-cognitive encoder
dest2
Encoding scheme was proposed that exploits
cognition and is optimal in certain scenarios
13
Information Theory for Mobile Ad-Hoc Networks
(ITMANET) The FLoWS Project
Thrusts 12
14
Relaying for Multiple Communicating PairsIvana
Maric, Ron Dabora and Andrea Goldsmith
ACHIEVEMENT DESCRIPTION
Several relaying strategies for forwarding
information to a single receiver
exist Capacity of networks are still unknown
one of the key obstacles how to handle and
exploit interference? How to relay for
multiple sources?Traditional approach routing

1) Interference forwarding can increase rates

• MAIN ACHIEVEMENT
• 1) Achievable rate region for the interference
  channel with a relay channel
• 2) Strong interference conditions under which
  forwarding messages and interference achieves
  capacity
• 3) A new sum-rate outer bound to the
  performance
• HOW IT WORKS
• The relay forwards an unwanted message, thus
  increasing the interference at the receiver. This
  allows the receiver to decode and cancel the
  interference.
• For the outer bound a genie enables receiver to
  decode both messages
• ASSUMPTIONS AND LIMITATIONS
• The considered channel model the interference
  channel with a relay
• Simple encoding schemes investigated

STATUS QUO
IMPACT
2) A tighter outer bound
In networks with multiple sources, relays can
help beyond forwarding useful information, by
increasing interference at the receivers. This
allows receivers to decode the interference and
cancel it prior to decoding their desired messages
NEXT-PHASE GOALS
dest1
source 1

• Consider interference forwarding in combination
  with other encoding strategies
• Apply interference forwarding and the outer
  bound to larger networks

relay
NEW INSIGHTS
dest2
source 2
A relaying strategy for networks with multiple
sources that can improve rates and achieve
capacity in certain scenarios proposed. A
tighter sum-rate bound on the performance
developed.
15
Cooperation and cognition in MIMO cognitive
networksYing Chang and Andrea Goldsmith
We derive the optimal achievable
rate for MISO secondary users under coexistence
constraints We propose practical strategies for
cognition and cooperation in MIMO systems We
find the relation between secondary users
achievable rate and primary users power
allocation scheme

• MAIN ACHIEVEMENT
• HOW IT WORKS
• Secondary user has non causal knowledge of
  primary users transmission and performs
  cognition together with cooperation to compensate
  the interference to primary receiver.
• We study the cases with MISO and MIMO
  secondary transmission system and multiple
  primary receivers.
• ASSUMPTIONS AND LIMITATIONS
• Primary users transmission rate is unchanged

Single-primary-user cognitive network
Multi-primary-user cognitive networks
System model We consider a MIMO cognitive network
as shown below. The cognitive transmitter
determines its codeword as a function of the
messages mp and mc .
In this case, the primary transmitter broadcasts
to several primary receivers. To maintain the
capacity region of primary users, the cognitive
user cooperate with each primary receiver. Power
allocation scheme is developed for MISO and MIMO
cognitive user. When the capacity region of the
primary broadcast channel is achieved, the
transmission rate for the cognitive user is as
follows Interestingly, we find out the
relation between the primary users sum rate and
cognitive users transmission rate is not
monotonic.
In literature, achievable rates of
single-antenna secondary user is well
studied How to do cooperation and cognition
with multiple antennas and multiple primary users
is our main focus
MISO , single primary user
MIMO Single primary user
MISO multiple primary users
Decompose the MIMO channel into orthogonal
components and leverage secondary users
beneficial and deteriorative impact to the
primary user. Introduce cooperation to
broadcast system
How to utilize new degrees of freedom brought by
MIMO technique?
To not impact the transmission rate of primary
(licensed) user, the cognitive user performs
cooperation to compensate the interference it
causes to the primary user. Encoding rule for
the cognitive user The cognitive encoder acts in
two stages. For every message pair (mp, mc), the
cognitive encoder first generates a codeword for
the primary message mp. In the second stage, the
cognitive encoder generates a codeword for mc
using Costa pre-coding. The two codewords are
superimposed to form the cognitive codeword.
Study multiple primary receivers with multiple
antennas Information theoretical bounds on MIMO
cognitive networks
In MIMO networks, we are more flexible to deal
with interference
MISO cognitive user In this case, we have a MISO
cognitive transmission pair. We propose an
optimal transmission strategy for the cognitive
user which projects its beamforming vector onto
orthogonal and aligned channel components. The
relation between the primary users rate and
cognitive users rate is as follows

• MIMO cognitive user
• In this case, we have a MIMO cognitive
  transmission pair. We propose two sub-optimal
  transmission strategies for the cognitive user
• Direct Channel SVD (D-SVD)
• The precoding matrix is obtained from the SVD of
  the cognitive users channel
• Projected Channel SVD (P-SVD)
• The cognitive users channel is projected onto
  the null space of the channel between the
  cognitive transmitter and primary receiver. Than
  SVD is performed on the projection.
• Under different power constraint, the
  performances of the two strategies are compared
  with the MIMO channel capacity.

16
On Networks with Side InformationA. Cohen, S.
Avestimehr and M. Effros

• Tight results for several families of networks
  with side information.
• A wider range of scenarios where cut-set analysis
  applies.
• An interesting and fruitful connection to
  successive refinement of information.

• MAIN ACHIEVEMENT
• New inner and outer bounds were derived for
  networks with side information.
• The bounds are tight
• for several network
• topologies.
• HOW IT WORKS
• Converse results for the canonical problem are
  generalized to multi-node networks.
• The achievable schemes are used at the terminals
  (sources and sinks), together with network
  coding.
• Successive refinement of both the source and side
  information descriptions is used when there are
  multiple sinks.
• ASSUMPTIONS LIMITATIONS
• One source node one helper.
• Bounds are not tight in general.

To large extent, our knowledge of networks with
side information is limited to the model above.
However, we are interested in more complex
networks

• Canonical source coding problems can be used to
  derive bounds for more complex networks.
• Network coding can play a key role even in
  non-multicast problems.

Extend this methodology to various source coding
problems. Derive new bounds and find network
topologies for which they are tight. Different
demand models(e.g. distortion)
Strategies intended for small problems, joint
with network codes, can solve complex networks
17
Feedback and Network CodingEffros and Bakshi
Increase in capacity is potentially
unbounded. Power consumption by remote sources
can be decreased by employing feedback from the
central receivers.

• MAIN ACHIEVEMENT
• In several examples networks, the capacity with
  feedback is strictly bigger than that without
  feedback
• - Butterfly network
• - Source coding with coded side information
• - Multiterminal source coding
• HOW IT WORKS
• Receiver sends back everything it knows to the
  transmitter nodes.
• e.g.
• - Encoder 2 knows X after the feedback.
• - Sum rate required is only H(X)
• ASSUMPTIONS AND LIMITATIONS
• Feedback links are assumed to have infinite
  capacity
• Sources nodes are assumed to have sufficient
  processing power

In todays networks, bulk of transmission from
sources to sinks Remote sources have often
lesser power available than sinks Feedback is
studied mostly in the context of channel
knowledge, not source knowledge
Feedback increases the capacity region. By
knowing what the receiver already knows from
other sources, source nodes can avoid unnecessary
transmission.
Cost of feedback?. Feedback links may not
always be free
Feedback increases the capacity of networks
18
Multicast Capacity Region of a Large Wireless
NetworkUrs Niesen Piyush Gupta Devavrat Shah

• Optimal two-layer network co-operative scheme for
  any traffic demand built on multi-hop and
  hierarchical scheme
• Geometry of capacity region it is nice and round

• MAIN ACHIEVEMENT
• Characterization of dim. multicast
  region
• Easily computable in terms of 2n weighted cuts
• Under Gaussian fading channel model
• HOW IT WORKS
• Achievability
• Realize tree network using co-operative relay
  built on multi-hop and hierarchical (virtual MAC
  and BC) depending upon channel characteristics
• Use this as multicast tree
• Converse
• Establish tightness of 2n cuts, each of them
  corresponds to a node of tree
• ASSUMPTIONS AND LIMITATIONS
• Random node placement

• Very little known about multicast capacity region
  of wireless network of n nodes
• It is dimensional
• Lack of fundamental understanding of
  co-operative relay schemes

• Equivalence relation
• Wireless network tree-structure
• This decides optimal structure for network-wide
  co-operation

• Multicast capacity scaling
• Arbitrary node placement

Complete characterization of multicast capacity
region separation of NET and PHY layer
19
Information Theory for Mobile Ad-Hoc Networks
(ITMANET) The FLoWS Project
Thrust 3
20
Relaxation Techniques for Net Opt W. Chen
S. Meyn

• Implementation Consensus algorithms
  Information distribution
• Adaptation Reinforcement learning techniques
• Integration with Network Coding projects
  Code around network hot-spots

What is the state of the art and what are its
limitations? Notes from Austin MW routing
inflexible, and does not easily incorporate
multi-access capacity region in
wireless. Workload relaxation techniques
Tremendous value for policy synthesis based on
dynamic hot-spots in the network Can these
techniques be extended to wireless models?
MAIN RESULT
Numerical findings With many flows, the rate
region appears smooth even in a static
interference model
Impact Network cut is no longer a useful concept
Infinite complexity leads to simple solution
Dynamics of 720 queues Half space relaxation
provides

• KEY NEW INSIGHTS
• Extend to wireless? YES Geometric picture is
  very different. Interpretation The number of
  resources is infinite
• Structure of optimal solution to relaxation is
  very simple, even for very complex networks
• New application of relaxation Q-learning and
  TD-learning for routing and power control

• Lower bound on performance and
• Tools for policy synthesis

HOW IT WORKS Step 1 Estimate capacity region
near estimated allocation rate vector Step 2
Construct ellipsoidal, and half-space
relaxations Step 3 Optimal policy for
relaxation, and interpret for original network

• Un-consummated union challenge Integrate
  coding and resource allocation
• Generally, solutions to complex decision
  problems should offer insight

Algorithms for dynamic routing Visualization and
Optimization
21
Stochastic resource allocationBoyd and Akuiyibo

• MAIN RESULT
• Explicit optimal control laws for resource
  allocation in a system with quadratic cost,
  linear dynamics, and random linear constraints.
• ASSUMPTIONS AND LIMITATIONS
• Assumes that the first and second moments of the
  resources are known
• Utility is quadratic dynamics must be linear

Stochastic allocation of competing network
resources i.e., bandwidth, power, flow rates,
etc. Simple control laws (linear coefficients can
be computed ahead of time).
Current resource allocation research focus on
iterative methods. These automatically adapt to
changing data assuming they are held constant.
Target value, x 6
averaging input algorithm
greedy algorithm trajectory
optimal trajectory

• Formulate as stochastic control problem
• Resource limits are random
• Allocate resources based on availability and
  system state

Utility maximizing estimation techniques
Decentralized solutions
Optimal dynamic resource allocation with
heterogeneous flows
22
A Distributed Newton Method for Network
Optimization Jadbabaie and Ozdaglar
Significant performance improvements
with the distributed Newton method compared to
standard subgradient methods.

• MAIN ACHIEVEMENT
• We developed a Newton method that solves network
  optimization problems in a distributed manner.
• We provide convergence and rate of convergence
  guarantees for the proposed method.
• Simulation experiments on a series of randomly
  generated graphs suggest superiority of the
  distributed Newton method over dual subgradient
  methods.
• HOW IT WORKS
• Constrained Newton method
• Dual Newton step found by solving a discrete
  Poisson equation involving the graph Laplacian.
• Using a consensus-based local averaging scheme,
  this can be done using only local information.
• ASSUMPTIONS AND LIMITATIONS
• Solves minimum cost network flow problems
• Extension to network utility maximization

All existing distributed optimization methods
rely on dual decomposition and subgradient (first
order) algorithms These algorithms easy to
distribute However, they can be quite slow to
converge limiting their use in rapidly changing
dynamic wireless networks.

• Second order methods for distributed network
  optimization
• Suggests an extensive research agenda for the
  investigation of these methods in decentralized
  environments

Combine Newton (second order) methods with
consensus policies to distribute the computations
associated with the dual Newton step
Distributed Second Order Methods with Convergence
Guarantees
23
Distributed Scheduling and Equilibrium Dynamics
in Wireless Networks with Correlated Fading
Channels (Candogan, Menache, Ozdaglar, Parrilo)

• Robust system design in the presence of
  non-cooperative users utilizing the desirable
  properties of potential games.

• Game-theoretic scheduling models allow the
  flexibility to incorporate different user
  objectives and arrive at an efficient operating
  point in a distributed manner.
• Correlated channel states are more realistic than
  existing models as they incorporate joint fading
  effects.

• Achievements
• Game-theoretic analysis of a distributed approach
  to scheduling that adapts to dynamically varying
  channel conditions.
• Simple convergent distributed dynamics and
  equilibrium characterization.
• Efficiency loss analysis suggests that finer
  state quantization can improve equilibrium
  performance.
• How it works
• Design incentives for the mobiles to project the
  game onto an (exact) potential game with
  desirable properties (such as convergence of
  simple dynamics)?
• Improved bounds on equilibrium performance can be
  obtained as a function of a technology related
  system parameter.
• Assumptions and limitations
• Full correlation across individual channel state
  processes.
• Fixed number of users and an uplink scenario.

Equilibrium

• Combine tools from optimization and game theory
• Potential games allow establishing existence and
  uniqueness of equilibrium, and convergence of
  simple distributed algorithms.

Example Collision Channel with two users. The
resulting game is an ordinal potential game with
two equilibria (TX, I) (I, TX)?

• Partial channel state correlation
• Projection of general games to ordinal potential
  games
• Convergence of dynamics with asynchronous updates
• Multi-hop network topologies

Local components (buildings)?
A potential game approach for distributed
scheduling in wireless networks
24
A Game Theoretic Approach to Network
CodingMarden and Effros
Approach provides guarantees independent of
network structure. Guarantees existence of an
equilibrium that achieves a system cost of at
most 50 higher than the optimal. This offers an
improvement over opportunistic coding.

• MAIN ACHIEVEMENT
• Introduced game theory as a distributed tractable
  mechanism to obtain good network performance
• HOW IT WORKS
• Model interactions as a non-cooperative game
• - players (unicast flows)
• - actions (available paths)
• Assign each player a cost function
• Analyze efficiency of equilibrium behavior
• ASSUMPTIONS AND LIMITATIONS

Global Objective Efficiently use network using
network coding Approach Centralized solutions.
(e.g., opportunistic coding) Fix paths, use
coding opportunities if available
Understand the potential of game theory in
network coding problems
Establish desirable distributed learning
algorithms with good convergence rates Extend
game theoretic approach to more general network
coding problems
What about distributed solutions? What if flows
were allowed to select path in response to local
cost? Goal Let users create coding
opportunities to improve efficiency
Game theory is an applicable tool for distributed
optimization in network coding
25
Oblivious equilibrium for stochastic games with
concave utilityS. Adlakha, R. Johari, G.
Weintraub, A. Goldsmith

MAIN RESULT Consider stochastic games
per-period utility and state dynamics that are
increasing, concave, submodular. Then in a large
system, each node can find approximately optimal
policies by treating the state of other nodes as
constant. HOW IT WORKS Under our
assumptions, no single node is overly influential
)we can replace other nodes states by their
mean.So the optimal policies decouple between
nodes. ASSUMPTIONS AND LIMITATIONS This result
holds under much more general technical
assumptions than our early results on the
problem. A key modeling limitation, however, is
that the limit requires all nodes to interact
with each other.Thus the results apply only to
dense networks.

• Our results provide a general framework to study
  the interaction of multiple devices.
• Further, our results
• unify existing models for which such limits were
  known
• and provide simple exogeneous conditions that
  can be checked to ensure the main result holds

Next state
Utility
Current state orcurrent action
Current state orcurrent action
Many cognitive radio models do notaccount for
reaction of other devicesto a single devices
action. In prior work, we developed a
generalstochastic game model to tractably
capture interactions of many devices.
of other devices withgiven state
In principle, tracking state of other
devices is complex. We approximate state of other
devices via a mean field limit.
State
We will apply our results to a modelof
interfering transmissions among
energy-constrained devices. Our main goal is to
develop arelated model that applies when a
single node interacts with a small number of
other nodes each period.
Real environments are reactive and
non-stationarythis requires new game-theoretic
models of interaction
26
Fluid limits for gossip processesV. Manshadi and
R. Johari

MAIN RESULT We consider a random graph
model where each nodehas d neighbors, and we
consider a limit where thenumber of nodes N
approaches infinity. We prove that the (random)
sample path of themicro model converges to the
(deterministic) pathof the corresponding macro
model. HOW IT WORKS We approximately
characterize howinformation flows in the micro
model between the sets of informed and uninformed
nodes. This approximation is exact as N !
infinity. ASSUMPTIONS AND LIMITATIONS Our
results currently only apply under specific
topological assumptions.
Micro and macro models of gossip processes have
been available for several decades. Unifying
these will allow us to translate macro-level
control insights to micro-level system designs.
Gossip is a simple model for communication
between nodesat random times, each node
contacts a neighbor and relays its
information. Prior work has studied the time
until all nodes acquire the information.Two
versions of this model a micro model and a
macro model.
Nodes that currently have the info
Nodes that currently do not have the info

• Several goals
• Extend fluid analysis to include heterogeneous
  random graphs.
• Get finer understanding of behavior when initial
  number of informed nodes is constant as N !
  infinity.
• Extend the model to include link failures.

The micro model tracks exactly which nodes have
the information. The macro model is a mean field
limit what fraction of nodes have learned the
information? We connect these two models.
The simplicity of macroscopic models for
information gossipcan be combined with the
accuracy of microscopic stochastic models
27
Information Theory for Mobile Ad-Hoc Networks
(ITMANET) The FLoWS Project
Thrusts 1,2,3
28
Queuing analysis for coded networks with
feedbackJ. Sundararajan, D. Shah, M. Médard, M.
Mitzenmacher, J. Barros

• Consequences.
• Queue size now grows linearly with 1/(1- ?)
• Reduces the amount of storage needed at
  intermediate nodes for performing re-encoding
• Analysis also applies when only some nodes do
  re-encoding
• ACK of degrees of freedom allows traditional
  queuing results to be applied easily in scenarios
  with network coding

Packets can be dropped from queue only upon
confirmation of decoding This means the queue
sizes will be unnecessarily long In particular,
as load factor ? approaches capacity, queue grows
quadratically as a function of 1/(1- ?)

• MAIN ACHIEVEMENT
• Propose novel ACK mechanism that allows nodes to
  manage queue occupancy effectively
• Characterize expected queue size at each node

HOW IT WORKS Acknowledge seen packets

• Key insight.
• With drop-when-decoded, the busy period of the
  virtual queue contributes to the physical queue
  size calculation
• Responding to ACK of the degrees of freedom
  ensures only queuing delay of virtual queues
  contributes to physical queue size

Almost as if there is link-by-link feedback
Extend queue management protocol to more general
(wireless) scenarios Multipath routing with
coding Multicast traffic pattern

• ASSUMPTIONS AND LIMITATIONS
• Perfect and delay-free feedback used in analysis,
  though not critical for the approach
• Field size assumed to be very large

The proposed approach to queue management will
play a key role in interfacing TCP with network
coding, especially when intermediate nodes
re-encode
29
Scheduling for Network Coded MulticastMedard,
Traskov, Heindlmaier, Koetter
No systematic approach to multi-access for
network coding.

• Shows that the performance of well-known
  scheduling techniques is very poor.
• Suggests a largely improved bandwidth
  efficiency.
• New notion of scheduling conflicts, when network
  coding is used.

• MAIN ACHIEVEMENT
• Hyperarc scheduling outperforms well-known
  scheduling techniques.
• HOW IT WORKS
• Valid network configurations can be identified as
  stable sets in the conflict graph.
• Jointly solve subgraph selection and scheduling
  problem.
• Distributed algorithm.
• ASSUMPTIONS AND LIMITATIONS
• Convergence speed of algorithm.

Current scheduling techniques use the bandwidth
very inefficiently.

• Graphical model for conflicts between hyperarcs.
• Do not try to minimize the number of collisions
  per se.

Extension to INTER-session network coding.
Investigations on performance/complexity
trade-offs.
Scheduling matched to the network coding subgraph
largely improves performance.
30
Interference-Mitigating Mobility Strategies in
MANETs Naini and Moulin

• Identifying the two-fold role of relays as
• being part of the source- receiver link
• conveying information about interferers signal
• Optimal mobility patterns could be used to gain
  insight into
• Optimal relay placement
• Positioning of nodes in coexistent interfering
  networks.

• MAIN RESULT
• Derived optimal interference-mitigating
  strategies for receiver node in a network with
  fixed relays
• Cut-set bound on capacity used as the
  cost-function.
• Saddle point strategies are feasible for the
  receiver and interferer.
• ASSUMPTIONS AND LIMITATIONS
• Greedy mobility strategy is assumed
• Nodes know neighboring nodes location and
  transmission power
• Surrogate capacity cost function is used

MANETs Focus has been mainly on mutual
interlinking and cooperation of nodes with
randomized mobility in the backdrop. Lack of
results on interference-mitigating mobility
strategies.

• Mobility should be seen as a resource to actively
  avoid interference from other nodes.
• Optimal mobility strategies can be established
  for nodes in noncooperative scenarios

Allow for relay mobility Include multi-hop
relaying Extension to non-greedy and
multi-objective cost function.
Exploit mobility to dynamically enlarge capacity
regions